Question

Do I get the right answers? If not, can someone please explain?

(a) 2 points possible (graded, results hidden) Consider a Gaussian linear model Y = aX + e in a Bayesian view. Consider the prior (a) = 1 for all a eR. Determine whether each of the following statements is true or false. (a) is a uniform prior. O True C False n(a) is a Jeffreys prior when we consider the likelihood L (Y = y|A = a, X = x) (where we assume x is known). O True C False (b) 3 points possible (graded, results hidden) Consider a linear regression model Y = Xß+ oe where E E R" is a random vector with E [e] = 0, E [ee' ] = I,n, and no further assumptions are made about e X is an n by p deterministic matrix, and X X is invertible. 0 is an unknown constant. O Let B denote the least squares estimator of B in this context. Determine whether each of the the following statements is true or false. 1. B is the maximum likelihood estimator for B. O True C False 2. With the model written as Y = XB + ae, B has dimension 1 xp (i.e. is a row vector of length p). True O False 3. В has a Gaussian distribution (even for small n). True O False

Answer 1

(a) correct (b) B is maximum likelihood estimator provided where In is identity matrix of order Since there is no 3. Hence the statement is False 2. Correct 3. Correct Nn(0, In) n. can't get MLE of further assumptions are made on e so we